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It’s the Friday Puzzle!

Please do NOT post your answer, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

On Christmas Day my brother and I opened our presents, and then noticed a curious coincidence. If I were to give my bother seven of my presents, then I would have exactly as many presents as my bother. On the other hand, if my brother were to give me seven presents, then I would have exactly twice as many presents as my brother. How many presents did each of us have?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

I’m afraid most people will get a pencil and paper and then do it the way they learned in school. It would be more fun to try to do it in your head, like Mike tried. But our heads are too small (as Mike discovered) so it would make sense to start by replacing the number 7 with something a lot smaller. Then it amazingly can fit in our heads.

Stan’s comment actually indicates the basic structure behind this problem. As long as it is the same and double requirement that is used for every one of these scenarios, the base is the same and all that really changes is that number that is subtracted or added. The result is related directly by that number whether you subtract seven or one. Really interesting. Thanks Stan.

2 mins: (i) looked for obvious shortcut/trap (ii) figured out the equations, (iii) solved using longhand — I’m too rusty to do this in my head nowadays.

@Bakers Dozen. I did my GCEs 47 & 45 yrs ago, so I find these useful by forcing me to actually make use of what was then in the O level syllabus. Has this really been upgraded to A level, or was that written in error?